Instructor

Prof. T. Mishonov

Course description

With the 2003 awarding of A. Abrikosov, V. Ginzburg, and A. Legett physics of superconductivity has won its 5th Nobel Prise and set in as a fundamental field and a continuous source of promising technological applications. The first part of the course will introduce the basic notions and consider the general electrodynamic and thermodynamic properties of superconductors, fluctuation phenomena in superconductors, the Ginzburg-Landau theory of superconductor surface tension, and Abrikosov's theory of the vortex state in superconductors. As a next step the ultimate technological applications will be considered: superconducting magnets, magnetic levitation, Josephson effect, metric standard for voltage unit, application of the Josephson effect for measuring weak magnetic fields, superconducting electromotors, generators and transformers using second-generation wires.

The next part of the course is dedicated to the Bardeen-Cooper-Schrieffer microscopic theory of superconductivity. This is similar in contents to the standard treatment given in the Landau, Lifchitz & Pitaevskii textbook and the monograph by Abrikosov. The final part of the course includes some advanced topics and is dedicated to the high-temperature superconductivity of the cuprate superconductors and MgB₂. Here, the pairing mechanism in these materials will be considered along with the main experiments used to determine their electronic spectrum. The course will conclude with consideration of the relation between superconductivity and magnetism. As an illustration, the Abrikosov spin-density wave (SDW) theory of the metal-insulator transition in the layered cuprates will be considered.

The course in its major part builds on the material taught at the bachelor level. This especially holds true for the basic experimental methods used in the physics of superconductivity. In the final part, however (making about 1:3 of the material), the course essentially exploits knowledge obtained from the courses in the Master program, such as Field Theoretical Methods in Solid Dtate Physics, and Quantum Field Theory. The last lectures will cover the latest achievements in this fast developing field. As a result, students will be able to follow the scientific publications in the field and even attempt scientific research.

Course Calendar/Schedule

Lecture/hours

1. General electrodynamic and thermodynamic properties of superconductors. Meissner effect, Kesom and Rutgers formulae for the specific heat and enthalpy of the superconducting transition / 3
2. London Electrodynamics, magnetic flux quantization, magnetic field penetration depth in superconductors. Experimental methods for probing the penetration depth: change of the resonance frequency of high-frequency resonators, muon depolarization, magnetization experiments. / 3
3. Ginzburg-Landau theory of the surface tension of type-I superconductors. Domain stricture, Silsby rule for the critical current. / 3
4. Abrikosov theory of the vortex state of superconductors. Upper critical field, nucleation field, magnetization curves, the Abrikosov vortex pinning as a method for achieving high critical currents and magnetic fields. Second generation superconducting wires and market perspectives for the superconducting wires, electromotors, generators and transformers. / 3
5. Josephson effect: an illustration of the idea for a macroscopic coherent state and application of the gauge invariance in quantum mechanics. Basic technological applications of the Josephson effect: metrological unit of voltage, and measuring weak magnetic fields. / 3
6. The microscopic Bardeen-Cooper-Schrieffer theory. Analysis of the derivation of the superconducting gap. Heuristic derivation due to Cooper. / 3
7. Bogolyubov variational approach / 2
8. Relation to the Green's function method in quantum field theory. Microscopic derivation of the electromagnetic response of superconductors. / 3
9. High critical temperature (high-T_c) superconductors -- the "blue dream" of physicists. Two-band superconductors, MgB₂ -- basic physical properties, theory of the specific heat and penetration depth. / 2
10. High-Tc cuprates. Electronic band structure of the CuO₂ plane. / 3
11. s-d model of the superconducting pairing. Angle-resolved photoemission spectroscopy (ARPES) as a major experimental method for probing the electronic spectrum of the layered cuprates. Theory of the superconducting gap anisotropy. / 3
12. The Abrikosov model for the spin-density waves and the metal-insulator transition in the layered cuprates. Relation between the magnetic phenomena and superconductivity. / 3
13. Superfluidity of He isotopes, Bose-Einstein condensation (BEC) and their relation to superconductivity. / 3
14. Hydrodynamics of superfluids and Bernoulli theorem. The Bernoulli effect as a means of measuring the effective mass of the Cooper pairs. / 3
15. Quantum Hall effect. Another example of electric current conduction without ohmic resistance and heating. Fractional Hall effect and its relation to challenging problems of mathematical physics. Integer quantum Hall effect and principles of operation of the metrological standard for resistance \Omega. / 3
16. Fluctuational phenomena in superconductors. Kinetics, and Boltzmann kinetic equation for the fluctuational Cooper pairs. / 3

Grading

The evaluation is made through an oral exam, but alternative forms are also possible: written exam, short research project resulting in an e-print uploaded to the arXiv server, or a manuscript submitted to a peer-reviewed scientific journal.

Textbooks

1. J. B. Keterson and S. N. Song, Superconductivity (Cambridge University Press, 1999)
2. E. M. Lifchitz and L. P. Pitaevskii, Statistical Physics Part II, Theory of condensed state (Moscow, Nauka, 1978,2001); Bulgarian translation available.
3. A. A. Abrikosov, Fundamentals of the theory of metals (North-Holland, Amsterdam, 1988)

Supplementary readings

1. T. M. Mishonov, J. O. Indekeu, and E. S. Penev, Superconductivity of overdoped cuprates: the modern face of the ancestral two-electron exchange, J. Phys.: Condens. Matter 15, 4429 (2003)
2. A. A. Abrikosov, Metal-insulator transition in layered cuprates (SDW model), Physica C 391, 147 (2003)